Calorimetry:
Energy Measurements
Measuring particles’ energies through
Electromagnetic and Hadronic interactions
Prof. Robin D. Erbacher
University of California, Davis
References: R. Fernow, Introduction to Experimental Particle Physics, Ch. 11
D. Green, The Physics of Particle Detectors, Ch. 11, 12
K. Kleinknecht, Ch. 6
http://pdg.lbl.gov/2004/reviews/pardetrpp.pdf
Introduction
Energy of a particle or group of particles is necessarily
measured destructively. We must completely stop the
particle in our detectors to measure its full energy.
The energy is deposited in a localized space, so that
position can be determined with accuracy dependent on
transverse energy fluctuations and detector design.
Accuracy of energy measurement comes from a:
• Constant term: Uniformity of the detector medium, and a
• Stochastic term: Level of active sampling wrt total detector volume
Calorimetry can thus provide momentum of a particle
redundantly to the inner tracking measurements, useful in
cleaning up backgrounds.
Multipurpose Calorimeters
Calorimeter use widespread, has become almost essential.
Neutral particles (s, neutrons) are only detected by this. Why?
Sampling calorimeters are sometimes used as  detectors.
Triggers for jets: as collision energies increase, particle
multiplicity increases, and we get highly collimated sprays
of secondary particles in a
localized angular distributions.
Can be made modular, and to
cover large solid angles. Size
scales as ln(E), but B-field
tracking goes like E1/2.
Partons  Particles  Jets
Processes creating jets
are very complicated, and
consist of parton
fragmentation, then both
electromagnetic and
hadronic showering in the
detector.
Reconstructing jets is,
naturally, also very
difficult. Jet energy scale
and reconstruction is one
of the largest sources of
systematic error.
More on Jets on Monday!
Electron and  Interactions
At E > 10 MeV, interactions of s and e-s in matter is
dominated by e+e- pair production and Bremsstrahlung.
At lower energies,
Ionization becomes
important.
The ratio of the
energy loss for
these processes is:
R
dE 
 
 dx Brem
Critical Energy:
When energy loss due to Brem and
energy loss due to ionization are =.
ZE
dE  ~
 
580MeV
 dx ion
580MeV
Ec 
Z
Electromagnetic Showers
An alternating sequence of
interactions leads to a cascade:
• Primary  with E0 energy pair-produces
with 54% probability in layer X0 thick
• On average, each has E0/2 energy
• If E0/2 > Ec, they lose energy by Brem
• Next layer X0, charged particle energy
decreases to E0/(2e)
• Brem of avg energy between E0/(2e) and
E0/2 is radiated
• Mean # particles after layer 2X0 is ~4
• Radiated s pair produce again
Cloud chamber photo of electromagnetic
cascade between spaced lead plates.
After n generations (dx= nX0), 2n particles, avg energy E0/2n for shower.
Cascade stops: e- energy  critical energy Ec= E0/2n.
Number of generations: n=ln(E0/Ec)/ln2.
Number of particles at shower maximum: Np = 2n = E0/Ec.
EM Shower Properties
Typical properties of electromagnetic showers:
• # particles at shower maximum Np proportional to E0
• Track length (depth) of e- and e+ proportional to E0
• Depth for maximum Xmax increases logarithmically:
Longitudinal energy deposition:
dE
 E 0ct  exp(t), where t  X / X 0 and
dt
  0.5,   t max , and c =   +1 /(  1)
vary logarithmically with energy
Transverse shower dimension:
multiple scattering of low energy e-:
Moliere Radius: RM  21 MeV  X0 / Ec
Longitudinal energy deposition for
e- in lead, fit to gamma function
Radial distribution in RM independent of material used!
99% of energy is inside a radius of 3 RM.
Energy Resolution
Energy resolution of ideal detector of infinite dimensions
is limited by statistical fluctuations.
Example: For Ec=11.8 MeV and detection cut-off Ek=0.5 MeV and a track
length of 176 cm/GeV, best resolution ~
 (E) / E  0.007/ E (GeV)
Losses of Resolution:
• Shower not contained in detector  
fluctuation of leakage energy;
longitudinal losses are worse than transverse leakage.
• Statistical fluctuations in number of photoelectrons observed in
detector. If  p N p / E 0 is # photoelectrons per unit primary particle E,
 (E) / E PE  1/ E 0
• Sampling
fluctuations if the counter is layered with inactive absorber.

• If active area is
 gas or liquid argon, low E e- move at large angles
from the shower axis, Landau tail leads to “path length fluctuations”.
Electromagnetic Calorimeter Types
Homogeneous “shower counters”:
Best performance from organic scintillating crystals. Example of NaI(Tl)
0.25
have achieved ~  (E) / E  0.028 /E (GeV ) . Also use lead glass, detects
Cerenkov light of electrons, limited by photoelectron statistics.
 calorimeters:
Sampling
Layers of inactive absorber (such as Pb) alternating with active detector
layers, such as scintillator or liquid. Resolutions ~7%/E or so.
Liquid noble gases:
Counters based on liquid noble gases (with lead plates, for example) can
act as ionization chambers. L Ar - Pb versions obtain ~10%/ E.
Ionization read out by electrodes attached to plates (no PMTs!).
Disadvantage: slow collection times (~1 s).
Variations in the 1990s: ‘Accordion’ for fast readout (front/back readout)
and L Kr homogeneous detector (energy&time resolution).
Electromagnetic Calorimeter Types
• “lead-scintillator sandwich” calorimeter
Energy resolutions:
E/E ~ 20%/√E
• exotic crystals (BGO, PbW, ...)
E/E ~ 1%/√E
• liquid argon calorimeter
E/E ~
Hadron Calorimeters
When a strongly interacting particle above 5 GeV enters
matter, both inelastic and elastic scattering between
particles and nucleons occur.
Secondary hadrons  examples: and K mesons, p and n.
Energy from primary goes to secondary, then tertiary, etc.
Cascade only ceases when hadron energies small enough
to stop by ionization energy loss or nuclear absorption.
Hadronic Shower: spatial scale for
material
X0 (g/cm2)
λn (g/cm2)
shower development given by nuclear
absorption length . Compare X0 for
high-Z materials, we see that the size
needed for hadron calorimeters is
large compared to EM calorimeters.
H2
Al
Fe
Pb
63
24
13.8
6.3
52.4
106
132
193
Compensating Calorimeters
Improvements in energy resolution can be achieved if
showers induced by electrons and hadrons of same
energy produce same visible energy (detector response).
Requires the losses to be “compensated” in some way.
Three methods:
1) Energy lost by nuclear reactions made up for by fission
of 238U, liberating n and soft rays. Can get response close to
equal: proton-rich detector em shower decreases, had shower
increases due to more nuclear reactions.
2) If have lots of H2, compensation achieved with high
absorber material: in inelastic collision of hadrons w/ absorber
nuclei, neutrons are produced  recoil protons, larger signal.
3) Reduce fluctuation in EM component: weight individual
counter responses, and even response out across the board.
CDF Sampling Calorimeter
• calorimeter is
arranged in projective
“towers” pointing at
the interaction region
• most of the depth is
for the hadronic part of
the calorimeter
CMS Hadron Calorimeter
Not Covered
• Shower shapes in hadron calorimeters
• Fluctuations in hadronic energy measurements
• Position resolution in the calorimeters
• Shower maximum detectors
• New calorimeter designs for ILC with silicon,
tracking for “particle-flow” algorithms.
Next Monday, Guest Lecture: Calibrating em and
hadron calorimeters, reconstructing jets, determining
the jet energy scale.
(Getting from calorimetry to physics results!)
Up next… Prof. Conway, statistics and data analysis
Example of Gaussian Distribution
• Single hit “residual” in silicon strip detector (distance from hit to
known track position):
Example of Binomial Statistics
• CDF track trigger efficiency:
Poisson Process
• Plot of observed tau lepton
pair mass
distribution in CDF:
• (Sorry, no Higgs yet…)
• Note difference between
linear and log scales!
The Higgs 2
• The most
famous plot in
high energy
physics…
• Tells us the
Higgs is close!
Complicated Confidence Interval
• All the world’s knowledge about the CKM matrix…